# WIN-U: Woodbury-Informed Newton-Unlearning as a retain-free Machine Unlearning Framework

arXiv: https://arxiv.org/abs/2604.13438 · HTML: https://mlsanity.com/paper/2604.13438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 28 of 28)

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- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Eight Methods to Evaluate Robust Unlearning in LLMs](https://mlsanity.com/paper/2402.16835/) (2024)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Continual Learning and Private Unlearning](https://mlsanity.com/paper/2203.12817/) (2022)
- [Unlearning or Obfuscating? Jogging the Memory of Unlearned LLMs via Benign Relearning](https://mlsanity.com/paper/2406.13356/) (2024)
- [OpenUnlearning: Accelerating LLM Unlearning via Unified Benchmarking of Methods and Metrics](https://mlsanity.com/paper/2506.12618/) (2025)
- [Do Unlearning Methods Remove Information from Language Model Weights?](https://mlsanity.com/paper/2410.08827/) (2024)
- [On Large Language Model Continual Unlearning](https://mlsanity.com/paper/2407.10223/) (2024)
- [Machine Unlearning: A Comprehensive Survey](https://mlsanity.com/paper/2405.07406/) (2024)
- [A Comprehensive Survey of Machine Unlearning Techniques for Large Language Models](https://mlsanity.com/paper/2503.01854/) (2025)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Hessian-Free Online Certified Unlearning](https://mlsanity.com/paper/2404.01712/) (2024)
- [A Certified Unlearning Approach without Access to Source Data](https://mlsanity.com/paper/2506.06486/) (2025)
- [Erase or Hide? Suppressing Spurious Unlearning Neurons for Robust Unlearning](https://mlsanity.com/paper/2509.22263/) (2025)
- [Gauss-Newton Unlearning for the LLM Era](https://mlsanity.com/paper/2602.10568/) (2026)

## Abstract (arXiv)

Privacy concerns in LLMs have led to the rapidly growing need to enforce a data's "right to be forgotten". Machine unlearning addresses precisely this task, namely the removal of the influence of some specific data, i.e., the forget set, from a trained model. The gold standard for unlearning is to produce the model that would have been learned on only the rest of the training data, i.e., the retain set. Most existing unlearning methods rely on direct access to the retained data, which may not be practical due to privacy or cost constraints. We propose WIN-U, a retained-data free unlearning framework that requires only second order information for the originally trained model on the full data. The unlearning is performed using a single Newton-style step. Using the Woodbury matrix identity and a generalized Gauss-Newton approximation for the forget set curvature, the WIN-U update recovers the closed-form linear solution and serves as a local second-order approximation to the gold-standard retraining optimum. Extensive experiments on various vision and language benchmarks demonstrate that WIN-U achieves SOTA performance in terms of unlearning efficacy and utility preservation, while being more robust against relearning attacks compared to existing methods. Importantly, WIN-U does not require access to the retained data.